{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZRHkD1pVPXd7"
      },
      "source": [
        "Copyright 2021 Google LLC\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "you may not use this file except in compliance with the License.\n",
        "You may obtain a copy of the License at\n",
        "\n",
        "    https://www.apache.org/licenses/LICENSE-2.0\n",
        "\n",
        "Unless required by applicable law or agreed to in writing, software\n",
        "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "See the License for the specific language governing permissions and\n",
        "limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LrRwIqX52kMs"
      },
      "source": [
        "## Notebook overview\n",
        "\n",
        "This notebook provides an interactive demonstration of adaptive dynamics prediction for rigid-body dynamics with data output from a PyBullet simulation of thrown objects. It describes the general structure of an adaptive predictor, mathematically constructs an adaptive predictor for rigid-body dynamics, and then provides an implementation."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8ZiqUNnKCyUt"
      },
      "outputs": [],
      "source": [
        "!pip install pybullet\n",
        "!pip install bullet"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yUm5-GSx4E52"
      },
      "outputs": [],
      "source": [
        "import pybullet as p\n",
        "import bullet as b\n",
        "import pybullet_data\n",
        "import numpy as onp\n",
        "import jax\n",
        "from jax import numpy as jnp\n",
        "from matplotlib import pyplot as plt\n",
        "import matplotlib as mpl\n",
        "import seaborn as sns\n",
        "import functools\n",
        "\n",
        "from jax import config\n",
        "config.update('jax_enable_x64', True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cjFCMRGO5ngc"
      },
      "source": [
        "### Imported Code"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7KSJ63bM6jXN"
      },
      "outputs": [],
      "source": [
        "\"\"\" Quaternion functions \"\"\"\n",
        "\n",
        "@jax.jit\n",
        "def skew(w):\n",
        "  w = jnp.reshape(w, (3))\n",
        "  return jnp.array([[0.0, -w[2], w[1]],\\\n",
        "                   [w[2], 0.0, -w[0]],\\\n",
        "                   [-w[1], w[0], 0.0]])\n",
        "\n",
        "@jax.jit\n",
        "def to_axis_angle(q):\n",
        "  angle = 2.0 * jnp.arccos(q[0])\n",
        "  axis = jnp.where(angle, q[1:] / jnp.sin(angle / 2.0), 0.0)\n",
        "  return (axis, angle)\n",
        "\n",
        "\n",
        "@jax.jit\n",
        "def normalize(q):\n",
        "  return q / jnp.linalg.norm(q)\n",
        "\n",
        "\n",
        "@jax.jit\n",
        "def multiply(q, p):\n",
        "  return jnp.concatenate((jnp.array([q[0] * p[0] - p[1:] @ q[1:]]),\n",
        "                         q[0] * p[1:] + p[0] * q[1:] + jnp.cross(q[1:], p[1:])))\n",
        "\n",
        "\n",
        "@jax.jit\n",
        "def vector_multiply(v, q):\n",
        "  \"\"\"Multiplication between quaternions [0, v0, v1, v2] and q.\"\"\"\n",
        "  return multiply(jnp.concatenate((jnp.array([0.0]), v)), q)\n",
        "\n",
        "\n",
        "@jax.jit\n",
        "def to_rotation_matrix(q):\n",
        "  (omega, theta) = to_axis_angle(q)\n",
        "  omega_sk = skew(omega)\n",
        "  return jnp.eye(3) + jnp.sin(theta) * omega_sk + (\n",
        "      1.0 - jnp.cos(theta)) * omega_sk @ omega_sk"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UZOlFBF655VC"
      },
      "outputs": [],
      "source": [
        "\"\"\" Potential functions for mirror descent \"\"\"\n",
        "\n",
        "@jax.jit\n",
        "def p_norm(x, p):\n",
        "  return .5*jnp.linalg.norm(x, p)**2\n",
        "\n",
        "\n",
        "@jax.jit\n",
        "def grad_p(x, p):\n",
        "  \"\"\"Direct calculation of the gradient of p_norm(x, p).\"\"\"\n",
        "  return jnp.linalg.norm(x, p)**(2-p)*jnp.abs(x)**(p-1)*jnp.sign(x)\n",
        "\n",
        "\n",
        "@jax.jit\n",
        "def inv_grad_p(x, p):\n",
        "  \"\"\"See https://arxiv.org/pdf/1912.13154.pdf, Section 8.1.\"\"\"\n",
        "  q = 1/(1 - 1/p)  # 1/q + 1/p == 1\n",
        "  return grad_p(x, q)\n",
        "\n",
        "\n",
        "@jax.jit\n",
        "def hypentropy(x, beta):\n",
        "  \"\"\"See https://arxiv.org/pdf/1902.01903.pdf.\"\"\"\n",
        "  return jnp.sum(x*jnp.arcsinh(x/beta) - jnp.sqrt(x**2 + beta**2))\n",
        "\n",
        "\n",
        "@jax.jit\n",
        "def grad_hyp(x, beta):\n",
        "  \"\"\"See https://arxiv.org/pdf/1902.01903.pdf.\"\"\"\n",
        "  return jnp.arcsinh(x/beta)\n",
        "\n",
        "\n",
        "@jax.jit\n",
        "def inv_grad_hyp(x, beta):\n",
        "  \"\"\"See https://arxiv.org/pdf/1902.01903.pdf.\"\"\"\n",
        "  return beta*jnp.sinh(x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FO5aRVVi5kQ7"
      },
      "outputs": [],
      "source": [
        "\"\"\"Class for adaptive dynamics prediction.\"\"\"\n",
        "\n",
        "from typing import Callable, Dict, Tuple\n",
        "\n",
        "@functools.partial(jax.jit, static_argnums=(0, 1))\n",
        "def rollout_prediction(norm_state: Callable[[jnp.ndarray], jnp.ndarray],\n",
        "                       predict_state: Callable[[jnp.ndarray, jnp.ndarray, int],\n",
        "                                               jnp.ndarray],\n",
        "                       params: jnp.ndarray, init_state: jnp.ndarray,\n",
        "                       t_range: jnp.ndarray) -\u003e jnp.ndarray:\n",
        "  \"\"\"Given a measurement, update the parameters and rollout the prediction.\n",
        "\n",
        "  Args:\n",
        "    norm_state: A function used to normalize the state after each step.\n",
        "    predict_state: A function mapping the current state estimate to the state\n",
        "    params: Current adaptive parameter estimates.\n",
        "    estimate at the next timestep.\n",
        "    init_state: Initial state for this rollout.\n",
        "    t_range: Range of discrete-time indices for the rollout.\n",
        "\n",
        "  Returns:\n",
        "    traj: The predicted state trajectory.\n",
        "  \"\"\"\n",
        "  def scan_fn(xhatt: jnp.ndarray, t: int) -\u003e Tuple[jnp.ndarray, jnp.ndarray]:\n",
        "    xhattp1 = norm_state(predict_state(xhatt, params, t))\n",
        "    return xhattp1, xhattp1\n",
        "\n",
        "  _, traj = jax.lax.scan(scan_fn, init_state, t_range)\n",
        "\n",
        "  return traj\n",
        "\n",
        "\n",
        "def euler(dynamics, dt):\n",
        "  def discretized(x, u, t):\n",
        "    return x + dt*dynamics(x, u, t)\n",
        "  return discretized\n",
        "\n",
        "\n",
        "def rk4(dynamics, dt):\n",
        "  \"\"\"RK4 discretization.\"\"\"\n",
        "  # dynamics(x, u, t)\n",
        "  def discretized(x, u, t):\n",
        "    k1 = dynamics(x, u, dt*t)\n",
        "    k2 = dynamics(x + dt*k1/2, u, dt*t + dt/2)\n",
        "    k3 = dynamics(x + dt*k2/2, u, dt*t + dt/2)\n",
        "    k4 = dynamics(x + dt*k3, u, dt*t + dt)\n",
        "    return x + dt*(k1 + 2*k2 + 2*k3 + k4)/6\n",
        "  return discretized\n",
        "\n",
        "\n",
        "def rk4_adaptive(dynamics, dt, sys_dim, inverse_mirror):\n",
        "  \"\"\"Discretize the adaptive system, applying the inverse mirror.\n",
        "\n",
        "  Note: this is basically a Runge-Kutta mirror descent. Because Runge-Kutta\n",
        "  evaluates the right-hand side at intermediate time points, we need to\n",
        "  re-apply the inverse mirror map to compute the parameters at intermeditate\n",
        "  time points.\n",
        "\n",
        "  Args:\n",
        "    dynamics: The dynamics to discretize\n",
        "    dt: The timestep.\n",
        "    sys_dim: System dimension (without adaptation parameters).\n",
        "    inverse_mirror: The inverse mirror map to apply to the parameters.\n",
        "\n",
        "  Returns:\n",
        "    The Runge-Kutta discretized mirror descent update.\n",
        "  \"\"\"\n",
        "  def discretized(xhat_and_mirror_params, ob, params, t):\n",
        "    k1 = dynamics(xhat_and_mirror_params, ob, params, dt*t)\n",
        "\n",
        "    xhat_and_mirror_params1 = xhat_and_mirror_params + dt*k1/2\n",
        "    p1 = inverse_mirror(xhat_and_mirror_params1[sys_dim:])\n",
        "    k2 = dynamics(xhat_and_mirror_params1, ob, p1, dt*t + dt/2)\n",
        "\n",
        "    xhat_and_mirror_params2 = xhat_and_mirror_params + dt*k2/2\n",
        "    p2 = inverse_mirror(xhat_and_mirror_params2[sys_dim:])\n",
        "    k3 = dynamics(xhat_and_mirror_params2, ob, p2, dt*t + dt/2)\n",
        "\n",
        "    xhat_and_mirror_params3 = xhat_and_mirror_params + dt*k3\n",
        "    p3 = inverse_mirror(xhat_and_mirror_params3[sys_dim:])\n",
        "    k4 = dynamics(xhat_and_mirror_params3, ob, p3, dt*t + dt)\n",
        "\n",
        "    return xhat_and_mirror_params + dt*(k1 + 2*k2 + 2*k3 + k4)/6\n",
        "\n",
        "  return discretized\n",
        "\n",
        "\n",
        "class AdaptivePredictor(object):\n",
        "  \"\"\"An adaptive dynamics predictor.\"\"\"\n",
        "  # system info\n",
        "  sys_dim: int\n",
        "  unknown_dim: int\n",
        "\n",
        "  # time info\n",
        "  # TODO(boffi): Reformulate this just in terms of the horizon of adaptation.\n",
        "  dt: float\n",
        "  nsteps: int\n",
        "  nframes: int\n",
        "  meas_count: int = 0\n",
        "  start_ind: int = 0\n",
        "  prediction_index: int\n",
        "\n",
        "  # adaptation parameter info\n",
        "  params: onp.ndarray\n",
        "  n_features: int\n",
        "  n_params: int\n",
        "\n",
        "  # adaptation terms\n",
        "  grad_psi_rf: Callable[[jnp.ndarray], jnp.ndarray]\n",
        "  inverse_grad_psi_rf: Callable[[jnp.ndarray], jnp.ndarray]\n",
        "  grad_psi_phys: Callable[[jnp.ndarray], jnp.ndarray]\n",
        "  inverse_grad_psi_phys: Callable[[jnp.ndarray], jnp.ndarray]\n",
        "\n",
        "  # continuous-time formulation\n",
        "  dynamics: Callable[[jnp.ndarray, jnp.ndarray, float], jnp.ndarray]\n",
        "  dynamics_with_measurement: Callable[\n",
        "      [jnp.ndarray, jnp.ndarray, jnp.ndarray, float], jnp.ndarray]\n",
        "\n",
        "  # discretized updates\n",
        "  predict_state: Callable[[jnp.ndarray, jnp.ndarray, int], jnp.ndarray]\n",
        "  predict_state_with_measurement: Callable[\n",
        "      [jnp.ndarray, jnp.ndarray, jnp.ndarray, int], jnp.ndarray]\n",
        "  norm_state: Callable[[jnp.ndarray], jnp.ndarray]\n",
        "\n",
        "  # stores the state prediction over the whole rollout\n",
        "  state_prediction: onp.ndarray\n",
        "\n",
        "  # pylint: disable=dangerous-default-value\n",
        "  def __init__(self,\n",
        "               predictor_continuous: Callable[[jnp.ndarray, jnp.ndarray, float],\n",
        "                                              jnp.ndarray],\n",
        "               measurement_function: Callable[[jnp.ndarray, jnp.ndarray],\n",
        "                                              jnp.ndarray],\n",
        "               adapt_continuous: Callable[\n",
        "                   [jnp.ndarray, jnp.ndarray, float, int], jnp.ndarray],\n",
        "               norm_state: Callable[[jnp.ndarray], jnp.ndarray],\n",
        "               ob: onp.ndarray,\n",
        "               init_params: onp.ndarray,\n",
        "               n_features: int = 0,\n",
        "               dt: float = 1e-3,\n",
        "               nsteps: int = 25,\n",
        "               nframes: int = 40,\n",
        "               potentials: Dict[str, str] = {\n",
        "                   'phys': 'euclid',\n",
        "                   'rf': 'euclid'\n",
        "               },\n",
        "               potential_params: Dict[str, float] = {\n",
        "                   'phys': 0.0,\n",
        "                   'rf': 0.0\n",
        "               },\n",
        "               prediction_index: int = 40) -\u003e None:\n",
        "    \"\"\"Initializes the adaptive predictor.\n",
        "\n",
        "    Args:\n",
        "        predictor_continuous: Continuous definition of the predictor.\n",
        "\n",
        "        measurement_function: Feedback measurement function g(x, hat{x}).\n",
        "\n",
        "        adapt_continuous: Continuous adaptation dynamics for physical basis\n",
        "        functions and random features.\n",
        "\n",
        "        norm_state: An optional state normalization to be applied after each\n",
        "        timestep, such as a quaternion projection.\n",
        "\n",
        "        ob: Initial observation of the system state.\n",
        "\n",
        "        init_params: Initialization for the adaptation parameters (both for\n",
        "        physical and for random features, physical first).\n",
        "\n",
        "        n_features: Number of random features.\n",
        "\n",
        "        dt: Timestep of the predictor.\n",
        "\n",
        "        nsteps: Number of steps of the predictor between measurements.\n",
        "\n",
        "        nframes: Define a frame as the number of between-measuremnent periods\n",
        "        over which the predictor will be active. nframes specifies the number\n",
        "        of frames so that with initialization, there are 1 + nframes*nsteps\n",
        "        total integration steps of the predictor.\n",
        "\n",
        "        potentials: Potential functions for physical and random feature\n",
        "          adaptation. Currently accepts 'euclid', 'p', and 'hyp' for euclidean,\n",
        "          p-norm, and hypentropy. Keys should be 'phys' and 'rf'.\n",
        "\n",
        "        potential_params: Parameters for the potentials (p value in the p norm\n",
        "        algorithm, beta value in hypentropy). Keys shold be 'phys' and 'rf'.\n",
        "\n",
        "        prediction_index: Past this point, we clamp the state to the observation\n",
        "        for maximally accurate predictions.\n",
        "    \"\"\"\n",
        "    self.sys_dim = ob.size\n",
        "\n",
        "    # initialize adaptation info\n",
        "    self.n_params = init_params.size\n",
        "    self.n_features = n_features\n",
        "\n",
        "    # prepare mirror maps.\n",
        "    self.setup_mirrors(potentials, potential_params)\n",
        "\n",
        "    # initialize time info\n",
        "    self.dt = dt\n",
        "    self.nsteps = nsteps\n",
        "    self.nframes = nframes\n",
        "    self.meas_count = 0\n",
        "    self.prediction_index = prediction_index\n",
        "\n",
        "    # construct the continuous formulation of the predictor\n",
        "    self.dynamics = predictor_continuous\n",
        "    self.setup_dynamics_with_measurement(measurement_function, adapt_continuous)\n",
        "\n",
        "    # construct discretized updates\n",
        "    self.predict_state = jax.jit(rk4(self.dynamics, self.dt))\n",
        "\n",
        "    self.predict_state_with_measurement = jax.jit(\n",
        "        rk4_adaptive(self.dynamics_with_measurement, self.dt, self.sys_dim,\n",
        "                     self.invert_mirrors))\n",
        "    self.norm_state = norm_state\n",
        "\n",
        "    # initialize the parameters\n",
        "    self.params = init_params\n",
        "\n",
        "    # initialize the predictor state\n",
        "    self.state_prediction = onp.zeros((nsteps*nframes + 1, self.sys_dim))\n",
        "    self.state_prediction[0, :] = ob\n",
        "\n",
        "  def setup_dynamics_with_measurement(\n",
        "      self,\n",
        "      measurement_function: Callable[[jnp.ndarray, jnp.ndarray],\n",
        "                                     jnp.ndarray],\n",
        "      adapt_continuous: Callable[[jnp.ndarray, jnp.ndarray, float, int],\n",
        "                                 jnp.ndarray]):\n",
        "    \"\"\"Initializes the dynamics_with_measurement() function.\"\"\"\n",
        "\n",
        "    def dynamics_with_measurement(xhat_and_mirror_params: jnp.ndarray,\n",
        "                                  ob: jnp.ndarray,\n",
        "                                  params: jnp.ndarray, t: float):\n",
        "      return jnp.concatenate(\n",
        "          (self.dynamics(xhat_and_mirror_params[:self.sys_dim], params, t) +\n",
        "           measurement_function(ob, xhat_and_mirror_params[:self.sys_dim]),\n",
        "           adapt_continuous(ob, xhat_and_mirror_params, t, self.sys_dim)))\n",
        "\n",
        "    self.dynamics_with_measurement = jax.jit(dynamics_with_measurement)\n",
        "\n",
        "  def setup_mirrors(self, potentials: Dict[str, str],\n",
        "                    potential_params: Dict[str, float]):\n",
        "    \"\"\"Sets up the forward and inverse mirror maps.\"\"\"\n",
        "    # pylint: disable=g-long-lambda\n",
        "    if potentials['phys'] == 'p':\n",
        "      self.grad_psi_phys = lambda x: grad_p(\n",
        "          x, potential_params['phys'])\n",
        "      self.inverse_grad_psi_phys = lambda x: inv_grad_p(\n",
        "          x, potential_params['phys'])\n",
        "    elif potentials['phys'] == 'hyp':\n",
        "      self.grad_psi_phys = lambda x: grad_hyp(\n",
        "          x, potential_params['phys'])\n",
        "      self.inverse_grad_psi_phys = lambda x: inv_grad_hyp(\n",
        "          x, potential_params['phys'])\n",
        "    else:\n",
        "      self.grad_psi_phys = lambda x: x\n",
        "      self.inverse_grad_psi_phys = lambda x: x\n",
        "\n",
        "    # set up mirror map for random feature parameters\n",
        "    if potentials['rf'] == 'p':\n",
        "      self.grad_psi_rf = lambda x: grad_p(\n",
        "          x, potential_params['rf'])\n",
        "      self.inverse_grad_psi_rf = lambda x: inv_grad_p(\n",
        "          x, potential_params['rf'])\n",
        "    elif potentials['rf'] == 'hyp':\n",
        "      self.grad_psi_rf = lambda x: grad_hyp(\n",
        "          x, potential_params['rf'])\n",
        "      self.inverse_grad_psi_rf = lambda x: inv_grad_hyp(\n",
        "          x, potential_params['rf'])\n",
        "    else:\n",
        "      self.grad_psi_rf = lambda x: x\n",
        "      self.inverse_grad_psi_rf = lambda x: x\n",
        "\n",
        "  def apply_mirrors(self, params: jnp.ndarray):\n",
        "    \"\"\"Applies the mirror maps to obtain auxiliary parameters.\"\"\"\n",
        "    return jnp.concatenate(\n",
        "        (self.grad_psi_phys(params[:self.n_params - self.n_features]),\n",
        "         self.grad_psi_rf(params[self.n_params -\n",
        "                                 self.n_features:self.n_params]),\n",
        "         params[self.n_params:]))\n",
        "\n",
        "  def invert_mirrors(self, mirror_params: jnp.ndarray):\n",
        "    \"\"\"Inverts the mirror maps to obtain the parameters.\"\"\"\n",
        "    return jnp.concatenate(\n",
        "        (self.inverse_grad_psi_phys(mirror_params[:self.n_params -\n",
        "                                                  self.n_features]),\n",
        "         self.inverse_grad_psi_rf(\n",
        "             mirror_params[self.n_params - self.n_features:self.n_params]),\n",
        "         mirror_params[self.n_params:]))\n",
        "\n",
        "  def rollout_prediction(self, t0: int) -\u003e jnp.ndarray:\n",
        "    \"\"\"Given a measurement, update the parameters and rollout the prediction.\n",
        "\n",
        "    Args:\n",
        "      t0: The initial time for the rollout.\n",
        "\n",
        "    Returns:\n",
        "      traj: The predicted state trajectory.\n",
        "    \"\"\"\n",
        "\n",
        "    # jax will have to re-jit rollout_adaption if the time horizon changes.\n",
        "    # to fix this, we rollout for nsteps*nframes timesteps every single time,\n",
        "    # and then only pick off the datapoints that we need.\n",
        "    return jax.device_get(\n",
        "        rollout_prediction(\n",
        "            self.norm_state, self.predict_state,\n",
        "            jax.device_put(self.params),\n",
        "            jax.device_put(self.state_prediction[t0, :]),\n",
        "            jnp.arange(\n",
        "                t0, t0 +\n",
        "                self.nframes * self.nsteps)))[:self.nframes * self.nsteps - t0]\n",
        "\n",
        "  def update_state(self, ob: jnp.ndarray) -\u003e None:\n",
        "    \"\"\"Given a measurement, updates the prediction and the parameters.\n",
        "\n",
        "    Args:\n",
        "      ob: The state observation.\n",
        "    \"\"\"\n",
        "    self.start_ind = self.meas_count * self.nsteps\n",
        "\n",
        "    # update the state and the mirrored parameters\n",
        "    jparams = jax.device_put(self.params)\n",
        "    init_state_and_mirror_params = jnp.concatenate(\n",
        "        (jax.device_put(self.state_prediction[self.start_ind, :]),\n",
        "         self.apply_mirrors(jparams)))\n",
        "\n",
        "    new_state_and_mirror_params = self.predict_state_with_measurement(\n",
        "        init_state_and_mirror_params, ob, jparams, self.start_ind)\n",
        "\n",
        "    # save the updated state. if we are before the place where we want\n",
        "    # to predict, just let the prediction keep going.\n",
        "    # otherwise, clamp the estimate to the observation for maximally accurate\n",
        "    # prediction.\n",
        "    time_to_predict = self.meas_count \u003e= self.prediction_index\n",
        "    if time_to_predict:\n",
        "      self.state_prediction[self.start_ind, :] = ob\n",
        "    else:\n",
        "      self.state_prediction[self.start_ind + 1, :] = jax.device_get(\n",
        "          new_state_and_mirror_params[:self.sys_dim])\n",
        "\n",
        "    # invert the mirror maps and compute the parameters\n",
        "    self.params = jax.device_get(\n",
        "        self.invert_mirrors(new_state_and_mirror_params[self.sys_dim:]))\n",
        "\n",
        "    if time_to_predict:\n",
        "      self.state_prediction[self.start_ind + 1:, :] = jax.device_get(\n",
        "          self.rollout_prediction(self.start_ind))\n",
        "    else:\n",
        "      self.state_prediction[self.start_ind + 2:, :] = jax.device_get(\n",
        "          self.rollout_prediction(self.start_ind + 1))\n",
        "\n",
        "    self.meas_count += 1\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2nBgpYsTWW9B"
      },
      "outputs": [],
      "source": [
        "# timestep of the simulation, and the predictor\n",
        "dt = 1e-3\n",
        "\n",
        "# set up the pybullet simulation environment\n",
        "p.connect(p.DIRECT)\n",
        "p.resetSimulation()\n",
        "p.setGravity(0, 0, -9.8)\n",
        "p.setTimeStep(dt)\n",
        "useFixedBase = True\n",
        "flags = p.URDF_INITIALIZE_SAT_FEATURES\n",
        "plane_pos = [0,0,-0.625]\n",
        "p.setAdditionalSearchPath(pybullet_data.getDataPath())\n",
        "plane = p.loadURDF('plane.urdf', plane_pos, flags = flags, useFixedBase=useFixedBase)\n",
        "sphere = p.loadURDF('sphere_small.urdf', [0, 0, 10], useMaximalCoordinates=True, flags=p.URDF_USE_INERTIA_FROM_FILE)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SLT55vPBOmHI"
      },
      "outputs": [],
      "source": [
        "def set_initial_state(object_id, position, orn, linear_velocity, angular_velocity):\n",
        "  \"\"\"Set the initial state of the robot.\"\"\"\n",
        "  p.resetBasePositionAndOrientation(object_id, position, orn)\n",
        "  p.resetBaseVelocity(object_id, linear_velocity, angular_velocity)\n",
        "\n",
        "def get_state(object_id):\n",
        "  \"\"\"Converts the pybullet state to a jax array matching the predictor order. \"\"\"\n",
        "  position, orientation = p.getBasePositionAndOrientation(object_id)\n",
        "  linear_velocity, angular_velocity = p.getBaseVelocity(object_id)\n",
        "\n",
        "  # make pybullet convention match jaxrobotics\n",
        "  orientation = jnp.array([orientation[3], orientation[0], orientation[1], orientation[2]])\n",
        "  position = jnp.array(position)\n",
        "  linear_velocity = jnp.array(linear_velocity)\n",
        "  angular_velocity = jnp.array(angular_velocity)\n",
        "\n",
        "  return jnp.concatenate((orientation, position, linear_velocity, angular_velocity))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sTd6t45zb1j-"
      },
      "source": [
        "# Adaptive prediction: general formulation\n",
        "A general adaptive predictor is specified as\n",
        "\n",
        "\\begin{align*}\n",
        "  \\dot{\\hat{\\mathbf{x}}} \u0026= \\mathbf{f}(\\hat{\\mathbf{x}}, t) + \\mathbf{Y}(\\hat{\\mathbf{x}}, t)_{\\text{phys}}\\hat{\\boldsymbol{\\alpha}}_{\\text{phys}} + \\mathbf{Y}(\\hat{\\mathbf{x}}, t)_{\\text{rf}}\\hat{\\boldsymbol\\alpha}_{\\text{rf}} + \\mathbf{g}(\\mathbf{x}, \\hat{\\mathbf{x}})\n",
        "\\end{align*}\n",
        "\n",
        "Above, $\\mathbf{f}(\\hat{\\mathbf{x}}, t)$ represents any part of the dynamics that is actually known. For example, as shown below, for rigid-body dynamics we know the dynamics of the orientation quaternion, and we also know the dynamics for two components of the velocity.\n",
        "\n",
        "$\\mathbf{g}(\\mathbf{x}, \\hat{\\mathbf{x}})$ is a measurement function used to incorporate a measurement when available.\n",
        "\n",
        "$\\mathbf{Y}(\\hat{\\mathbf{x}}, t)_{\\text{phys}}\\hat{\\boldsymbol{\\alpha}}_{\\text{phys}}$ represents a physical approximation with physical basis functions $\\mathbf{Y}(\\hat{\\mathbf{x}}, t)_{\\text{phys}}$ and corresponding parameters $\\hat{\\boldsymbol{\\alpha}}_{\\text{phys}}$.\n",
        "\n",
        "$\\mathbf{Y}(\\hat{\\mathbf{x}}, t)_{\\text{rf}}\\hat{\\boldsymbol\\alpha}_{\\text{rf}}$ represents a mathematical approximation with unstructured basis functions $\\mathbf{Y}(\\hat{\\mathbf{x}}, t)_{\\text{rf}}$ (for example, here chosen as random features) with corresponding parameters $\\hat{\\boldsymbol\\alpha}_{\\text{rf}}$\n",
        "\n",
        "The two parameter vectors are updated according to the continuous-time algorithm\n",
        "\n",
        "\\begin{align*}\n",
        "  \\frac{d}{dt}\\nabla\\psi_{\\text{phys}}\\left(\\hat{\\boldsymbol{\\alpha}}_{\\text{phys}}\\right) \u0026= - \\eta_p \\mathbf{Y}\\left(\\hat{\\mathbf{x}}, t\\right)_{\\text{phys}}^{\\mathsf{T}}\\mathbf{e}_{\\text{phys}}(\\mathbf{x}, \\hat{\\mathbf{x}}),\\\\\n",
        "  \\frac{d}{dt}\\nabla\\psi_{\\text{rf}}\\left(\\hat{\\boldsymbol{\\alpha}}_{\\text{rf}}\\right) \u0026= - \\eta_{\\text{rf}} \\mathbf{Y}\\left(\\hat{\\mathbf{x}}, t\\right)_{\\text{rf}}^{\\mathsf{T}}\\mathbf{e}_{\\text{rf}}(\\mathbf{x}, \\hat{\\mathbf{x}}),\n",
        "\\end{align*}\n",
        "\n",
        "Above, $\\psi_i$ represent mirror descent potentials used to regularize the two predictor dynamics, or to improve adaptation based on the geometry of the basis functions. \n",
        "\n",
        "$\\mathbf{e}_i(\\cdot, \\cdot)$ are error signals used to drive the adaptation\n",
        "\n",
        "$\\eta_i$ are two learning rates for the individual parameter vectos.\n",
        "\n",
        "Below, we provide a mathematical instantiation of this formulation for rigid-body dynamics, and subsequently implement that mathematical instantation.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TA51EfYrjFQo"
      },
      "outputs": [],
      "source": [
        "#### Adaptive predictor parameters\n",
        "# mirror descent potentials \\psi_i and parameters for those potentials.\n",
        "potentials       = {'phys': 'euclid', 'rf': 'euclid'}\n",
        "potential_params = {'phys': 1.0, 'rf': 1.0}\n",
        "\n",
        "# we define a frame as a sequence of steps between measurements.\n",
        "# number of predictor steps for each frame (steps between measurements) and number of total\n",
        "# frames (number of observations we receive over the course of the trajectory)\n",
        "nsteps = 25\n",
        "nframes = 40\n",
        "\n",
        "# learning rates\n",
        "eta_p = 10.0 * nsteps\n",
        "eta_rf = 20.0 * nsteps\n",
        "\n",
        "# measurement feedback gain, used in g(x, \\hat{x})\n",
        "k = 25 * nsteps\n",
        "\n",
        "# random feature info\n",
        "n_features = 50\n",
        "n_avg = 10\n",
        "input_dim = 6\n",
        "approx_dim = 3\n",
        "\n",
        "# initialize the parameters\n",
        "nparams = 18 + n_features\n",
        "init_params = onp.zeros(nparams)\n",
        "\n",
        "# strength of noise added to observations\n",
        "noise_str = 0.0\n",
        "\n",
        "# dimension of rigid-body dynamics\n",
        "sys_dim = 13"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dmcHCuKbffYt"
      },
      "source": [
        "# Adaptive prediction for rigid-body dynamics\n",
        "The rotational and translational motion of a rigid-body may be specified in continuous-time as\n",
        "\\begin{align}\n",
        "   \\dot{\\mathbf{q}} \u0026= \\frac{1}{2}\\mathbf{\\omega}\\circ\\boldsymbol{q}\\\\\n",
        "  \\dot{\\mathbf{p}} \u0026= \\mathbf{v}\\\\\n",
        "  \\dot{\\mathbf{v}} \u0026= -\\mathbf{g}\\\\\n",
        "  \\dot{\\boldsymbol\\omega} \u0026= - \\mathbf{J}^{-1}\\boldsymbol{\\omega}\\times\\mathbf{J}\\boldsymbol{\\omega}\n",
        "\\end{align}\n",
        "\n",
        "Above, $\\circ$ denotes the quaternion product, $\\times$ denotes the cross product, and $\\mathbf{J}$ is the moment of inertia matrix. Boldface denotes vectors and capital boldface denotes matrices. We have written the translational dynamics in the world frame, where they decouple from the rotational dynamics. We have written the rotational dynamics in the body frame, where the moment of intertia tensor becomes a constant. For simplicity, in this notebook, we assume that we receive measurements for the translational and rotational motion of the center of mass; measurements from a fixed location in the body can similarly be handled with additional complications. \n",
        "\n",
        "The unknown physical parameters are the components of $\\mathbf{J}$. Because the only unknown parameters are contained in $\\mathbf{J}$, we know the dynamics of $\\mathbf{q}$, $\\mathbf{p}$, and $\\mathbf{v}$.\n",
        "\n",
        "While the term $- \\mathbf{J}^{-1}\\boldsymbol{\\omega}\\times\\mathbf{J}\\boldsymbol{\\omega}$ is nonlinear in the unknown inertia matrix $\\mathbf{J}$, it can be written as a linear expansion in a set of parameters of larger dimension. \n",
        "\n",
        "\\begin{align}\n",
        "  \\dot{\\hat{\\mathbf{q}}} \u0026= \\frac{1}{2}\\hat{\\mathbf{\\omega}}\\circ\\hat{\\boldsymbol{q}} + k(\\mathbf{q} - \\hat{\\mathbf{q}})\\\\\n",
        "  \\dot{\\hat{\\mathbf{p}}} \u0026= \\hat{\\mathbf{v}} + k(\\mathbf{p} - \\hat{\\mathbf{p}})\\\\\n",
        "  \\dot{\\hat{\\mathbf{v}}} \u0026= -\\mathbf{g} + k\\left(\\mathbf{v} - \\hat{\\mathbf{v}}\\right)\\\\\n",
        "  \\dot{\\hat{\\boldsymbol\\omega}} \u0026= \\mathbf{Y}(\\hat{\\boldsymbol\\omega})\\hat{\\boldsymbol\\alpha}_{\\text{phys}} + k(\\boldsymbol\\omega - \\hat{\\boldsymbol\\omega})\n",
        "\\end{align}\n",
        "\n",
        "We have chosen a simple linear feedback term, $\\mathbf{g}(\\mathbf{x}, \\hat{\\mathbf{x}}) = k(\\mathbf{x} - \\hat{\\mathbf{x}})$.\n",
        "\n",
        "The physical parameters are upated according to\n",
        "\n",
        "\n",
        "\\begin{equation*}\n",
        "  \\frac{d}{dt}\\nabla\\psi_{\\text{phys}}\\left(\\hat{\\boldsymbol{\\alpha}}_{\\text{phys}}\\right) = - \\eta_p \\mathbf{Y}\\left(\\hat{\\mathbf{x}}, t\\right)_{\\text{phys}}^{\\mathsf{T}}\\left(\\hat{\\boldsymbol\\omega} - \\boldsymbol\\omega\\right)\n",
        "\\end{equation*}\n",
        "\n",
        "The error signal $\\mathbf{e}_{\\text{phys}}(\\mathbf{x}, \\hat{\\mathbf{x}}) = \\hat{\\boldsymbol\\omega} - \\boldsymbol{\\omega}$ because the parameter estimates $\\hat{\\boldsymbol{\\alpha}}_{\\text{phys}}$ only appear in the $\\dot{\\hat{\\boldsymbol\\omega}}$ dynamics.\n",
        "\n",
        "We may also add random features to the entire predictor. The parameters for this unstructured approximation would then be updated according to\n",
        "\n",
        "\\begin{equation*}\n",
        "  \\frac{d}{dt}\\nabla\\psi_{\\text{rf}}\\left(\\hat{\\boldsymbol{\\alpha}}_{\\text{rf}}\\right) = - \\eta_{\\text{rf}} \\mathbf{Y}\\left(\\hat{\\mathbf{x}}, t\\right)_{\\text{rf}}^{\\mathsf{T}}\\left(\\hat{\\mathbf{x}} - \\mathbf{x}\\right)\n",
        "\\end{equation*}\n",
        "\n",
        "Here, the error signal is given by the total error $\\mathbf{\\hat{x}} - \\mathbf{x}$ because we add the random feature approximation to the entire predictor. In general, if we plan to estimate disturbances in only a few components, the random feature adaptation can be driven by the error in those components and does not have to be a function of the full predictor state."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uCDjP1Bnzuwo"
      },
      "outputs": [],
      "source": [
        "grav = jnp.array([0., 0., -9.8])\n",
        "\n",
        "@jax.jit\n",
        "def world_to_body(q: jnp.ndarray, vec: jnp.ndarray) -\u003e jnp.ndarray:\n",
        "  \"\"\" Takes vec in the world frame and maps it to the body frame. \"\"\"\n",
        "  R = to_rotation_matrix(q).T\n",
        "  return  R @ vec\n",
        "\n",
        "@jax.jit\n",
        "def phys_error_signal(x: jnp.ndarray, xhat: jnp.ndarray) -\u003e jnp.ndarray:\n",
        "  \"\"\"Returns the error used in the adaptation for the inertial params.\n",
        "  Assumes that the measurements all come in in world coordinates.\"\"\"\n",
        "  q = x[:4]\n",
        "  w_world = x[10:]\n",
        "#  w = world_to_body(q, w_world)\n",
        "  w = w_world\n",
        "  what = xhat[10:]\n",
        "  return what - w\n",
        "\n",
        "@jax.jit\n",
        "def norm_state(xhat: jnp.ndarray) -\u003e jnp.ndarray:\n",
        "  \"\"\" State normalization via quaternion projection. \"\"\"\n",
        "  return jnp.concatenate((normalize(xhat[:4]), xhat[4:]))\n",
        "\n",
        "@jax.jit\n",
        "def inertial_basis(xhat: jnp.ndarray, t: float) -\u003e jnp.ndarray:\n",
        "  \"\"\" Overparameterized inertial basis matrix. \"\"\"\n",
        "  x, y, z = xhat[-3:]\n",
        "  inert_mat = jnp.array([\n",
        "      [x*z, y*z, x*y, x*x, y*y, z*z, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
        "      [0, 0, 0, 0, 0, 0, x*y, x*z, z*y, y*y, x*x, z*z, 0, 0, 0, 0, 0, 0],\n",
        "      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x*z, z*y, x*y, x*x, y*y, z*z]])\n",
        "  return inert_mat\n",
        "\n",
        "@jax.jit\n",
        "def measurement_function(x: jnp.ndarray, xhat: jnp.ndarray) -\u003e jnp.ndarray:\n",
        "  \"\"\"Measurement function.\"\"\"\n",
        "  q = x[:4]\n",
        "  w_world = x[10:]\n",
        "#  w = world_to_body(q, w_world)\n",
        "  w = w_world\n",
        "  obs = jnp.concatenate((q, x[4:10], w))\n",
        "  return k*(obs - xhat)\n",
        "\n",
        "def init_random_features(key: jnp.ndarray, approx_dim: int, input_dim: int, \n",
        "                         n_features: int, n_avg: int):\n",
        "  \"\"\"Constructs the random basis functions.\"\"\"\n",
        "  key, skey = jax.random.split(key)\n",
        "  w = jax.random.normal(skey, shape=(approx_dim, n_features, n_avg, input_dim))\n",
        "  key, skey = jax.random.split(key)\n",
        "  b = jax.random.uniform(skey, shape=(approx_dim, n_features, n_avg))\n",
        "  return lambda x: jnp.sum(jnp.cos(w @ x + b), axis=2)/jnp.sqrt(n_avg)\n",
        "\n",
        "# construct the random feature approximators\n",
        "key = jax.random.PRNGKey(0)\n",
        "key, skey = jax.random.split(key)\n",
        "rf_basis = init_random_features(skey, approx_dim, input_dim, n_features, n_avg)\n",
        "\n",
        "@jax.jit\n",
        "def rf_error_signal(x: jnp.ndarray, xhat: jnp.ndarray):\n",
        "  \"\"\" Error signal for random feature adaptation. \"\"\"\n",
        "  v, vhat = x[7:10], xhat[7:10]\n",
        "  return vhat - v\n",
        "\n",
        "@functools.partial(jax.jit, static_argnums=3)\n",
        "def adapt_continuous(x: jnp.ndarray, xhat_and_mirror_params: jnp.ndarray, t: float, sys_dim) -\u003e jnp.ndarray:\n",
        "  \"\"\"Continuous definition of the adaptive predictor.\"\"\"\n",
        "  xhat = xhat_and_mirror_params[:sys_dim]\n",
        "  vhat_and_what = xhat[7:]\n",
        "  phys_adapt = -eta_p* inertial_basis(xhat, t).T @ phys_error_signal(x, xhat)\n",
        "  rf_adapt = -eta_rf * rf_basis(vhat_and_what).T @ rf_error_signal(x, xhat)\n",
        "  return jnp.concatenate((phys_adapt, rf_adapt))\n",
        "\n",
        "@jax.jit\n",
        "def predictor_continuous(xhat: jnp.ndarray, params: jnp.ndarray, t: float) -\u003e jnp.ndarray:\n",
        "  \"\"\"Returns the dynamics predictor in continuous-time without measurement.\n",
        "  \n",
        "  Assumes that the state is given by:\n",
        "              (quaternion, position, velocity, angular velocity)\n",
        "  \n",
        "  Args:\n",
        "    xhat: Predicted state vector.\n",
        "    params: Current parameter estimates.\n",
        "    t: The current time.\n",
        "  \n",
        "  Returns:\n",
        "    The continuous-time dynamics.\n",
        "  \"\"\"\n",
        "  qhat = xhat[0:4]\n",
        "  vhat = xhat[7:10]\n",
        "  what = xhat[10:]\n",
        "  vhat_and_what = xhat[7:]\n",
        "  \n",
        "  qhat_dot = .5 * vector_multiply(what, qhat)\n",
        "  phat_dot = vhat\n",
        "\n",
        "  # add random features to velocity for estimation of magnus effect.\n",
        "  # magnus and lift depend on translational and angular velocity.\n",
        "  vhat_dot = grav + rf_basis(vhat_and_what) @ params[nparams - n_features:]\n",
        "  what_dot = inertial_basis(xhat, t) @ params[:nparams - n_features]\n",
        "  \n",
        "  return jnp.concatenate((qhat_dot, phat_dot, vhat_dot, what_dot))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LrVgHErJpgqt"
      },
      "source": [
        "The following code cell demonstrates how to construct an ```AdaptivePredictor``` object using the above implementation and how to use the predictor for rigid-body dynamics with PyBullet."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yEOA5XLDOPMN"
      },
      "outputs": [],
      "source": [
        "# set object for experiments\n",
        "object_id = sphere\n",
        "\n",
        "# set initial velocity and grab the initial measurement\n",
        "set_initial_state(object_id, [0, 0, 10.], [0, 0, 0, 1.], [1, 3, 2.], [3., 2., 1.])\n",
        "x_init = get_state(object_id)\n",
        "\n",
        "# construct the adaptive predictor\n",
        "predictor = AdaptivePredictor(predictor_continuous, measurement_function, adapt_continuous, norm_state, \n",
        "                              x_init, init_params, n_features, dt, nsteps, nframes, potentials, \n",
        "                              potential_params, prediction_index=nframes)\n",
        "\n",
        "# store the state of the predictor and the parameters over the entire trajectory.\n",
        "predictor_states = []\n",
        "params_over_time = onp.zeros((nframes, nparams))\n",
        "params_over_time[0, :] = init_params\n",
        "\n",
        "# store the pybullet state over time\n",
        "state_observations = onp.zeros((1+nsteps*nframes, 13))\n",
        "state_observations[0, :] = x_init\n",
        "\n",
        "# rollout the simulation\n",
        "state_observation = x_init\n",
        "for i in range(nsteps*nframes):\n",
        "  p.stepSimulation()\n",
        "\n",
        "  # incorporate the measurement and update the parameters\n",
        "  new_measurement = (i % nsteps) == 0\n",
        "  if new_measurement:\n",
        "    ind = int(i / nsteps)\n",
        "    predictor.update_state(state_observation + 2*noise_str*onp.random.uniform(size=13) - noise_str)\n",
        "    predictor_states.append(predictor.state_prediction.copy())\n",
        "    params_over_time[ind, :] = predictor.params\n",
        "\n",
        "  # save the state observations over time for direct comparison\n",
        "  state_observation = get_state(object_id)\n",
        "  state_observations[i+1, :] = state_observation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hzBKLdVspxH0"
      },
      "source": [
        "The following two code cells provide ```matplotlib``` defaults for nice-looking plots, as well as convenience functions for visualizing the performance of the predictor."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tvFZUQVjxEVY"
      },
      "outputs": [],
      "source": [
        "### figure parameters\n",
        "%matplotlib inline\n",
        "sns.set_style(\"white\")\n",
        "mpl.rcParams['axes.grid'] = True\n",
        "mpl.rcParams['axes.grid.which'] = 'both'\n",
        "mpl.rcParams['xtick.minor.visible'] = True\n",
        "mpl.rcParams['ytick.minor.visible'] = True\n",
        "mpl.rcParams['grid.color'] = '0.8'\n",
        "mpl.rcParams['axes.facecolor'] = 'white'\n",
        "mpl.rcParams['text.usetex'] = False\n",
        "mpl.rcParams['font.family'] = 'serif'\n",
        "\n",
        "cmap3 = sns.cubehelix_palette(n_colors=3, start=.5, rot=-.75, light=.6, dark=.15, hue=1, gamma=.95, reverse=False)\n",
        "cmap4 = sns.cubehelix_palette(n_colors=4, start=.5, rot=-.75, light=.6, dark=.15, hue=1, gamma=.95, reverse=False)\n",
        "cmap_ps = sns.cubehelix_palette(n_colors=nparams, start=.5, rot=-.75, light=.6, dark=.15, hue=1, gamma=.95, reverse=False)\n",
        "\n",
        "fs         = (8, 5)\n",
        "lab_size   = 20\n",
        "title_size = 20\n",
        "ticksize   = 20\n",
        "leg_size   = 20\n",
        "lw         = 2\n",
        "leg_alpha  = 0"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9khqiD8OdSXb"
      },
      "outputs": [],
      "source": [
        "### Visualization convenience functions.\n",
        "def make_prediction_comparison_plot(n_total_steps: int, dt: float, state_observations: jnp.ndarray, predictor_states: list, measurement_no: int, variable_name: str):\n",
        "  \"\"\"Produces a plot of the prediction and the prediction error, produced after receiving measurement measurement_no, for the state variables variable_name.\"\"\"\n",
        "  state_predictions = predictor_states[measurement_no]\n",
        "  times = dt*onp.arange(n_total_steps)\n",
        "  if variable_name == 'orientation':\n",
        "    fig, ax = plt.subplots(figsize=fs)\n",
        "    plt.plot(times, state_observations[:, 0], label=r\"$q_w$\", color=cmap4[0])\n",
        "    plt.plot(times, state_observations[:, 1], label=r\"$q_x$\", color=cmap4[1])\n",
        "    plt.plot(times, state_observations[:, 2], label=r\"$q_y$\", color=cmap4[2])\n",
        "    plt.plot(times, state_observations[:, 3], label=r\"$q_z$\", color=cmap4[3])\n",
        "    plt.plot(times, state_predictions[:, 0], label=r\"$\\hat{q}_w$\", color=cmap4[0], linestyle='--')\n",
        "    plt.plot(times, state_predictions[:, 1], label=r\"$\\hat{q}_x$\", color=cmap4[1], linestyle='--')\n",
        "    plt.plot(times, state_predictions[:, 2], label=r\"$\\hat{q}_y$\", color=cmap4[2], linestyle='--')\n",
        "    plt.plot(times, state_predictions[:, 3], label=r\"$\\hat{q}_z$\", color=cmap4[3], linestyle='--')\n",
        "    plt.axvline(x = dt*nsteps*measurement_no)\n",
        "    plt.ylabel(variable_name, fontsize=lab_size)\n",
        "    plt.xlabel('time', fontsize=lab_size)\n",
        "    plt.tick_params(axis='both', labelsize=ticksize)\n",
        "    ax.minorticks_on()\n",
        "    plt.tight_layout()\n",
        "    ax.grid(True, which='both')\n",
        "    plt.legend(fontsize=lab_size, ncol=4, framealpha=leg_alpha)\n",
        "\n",
        "    fig, ax = plt.subplots(figsize=fs)\n",
        "    plt.plot(times, state_predictions[:, 0] - state_observations[:, 0], label=r\"$\\tilde{q}_w$\", color=cmap4[0])\n",
        "    plt.plot(times, state_predictions[:, 1] - state_observations[:, 1], label=r\"$\\tilde{q}_x$\", color=cmap4[1])\n",
        "    plt.plot(times, state_predictions[:, 2] - state_observations[:, 2], label=r\"$\\tilde{q}_y$\", color=cmap4[2])\n",
        "    plt.plot(times, state_predictions[:, 3] - state_observations[:, 3], label=r\"$\\tilde{q}_z$\", color=cmap4[3])\n",
        "    plt.axvline(x = dt*nsteps*measurement_no)\n",
        "    plt.ylabel(variable_name + ' error', fontsize=lab_size)\n",
        "    plt.xlabel('time', fontsize=lab_size)\n",
        "    plt.tick_params(axis='both', labelsize=ticksize)\n",
        "    ax.minorticks_on()\n",
        "    plt.tight_layout()\n",
        "    ax.grid(True, which='both')\n",
        "    plt.legend(fontsize=lab_size, ncol=2, framealpha=leg_alpha)\n",
        "  elif variable_name == 'position':\n",
        "    fig, ax = plt.subplots(figsize=fs)\n",
        "    plt.plot(times, state_observations[:, 4], label=r\"$x$\", color=cmap3[0])\n",
        "    plt.plot(times, state_observations[:, 5], label=r\"$y$\", color=cmap3[1])\n",
        "    plt.plot(times, state_observations[:, 6], label=r\"$z$\", color=cmap3[2])\n",
        "    plt.plot(times, state_predictions[:, 4], label=r\"$\\hat{x}$\", color=cmap3[0], linestyle='--')\n",
        "    plt.plot(times, state_predictions[:, 5], label=r\"$\\hat{y}$\", color=cmap3[1], linestyle='--')\n",
        "    plt.plot(times, onp.maximum(0, state_predictions[:, 6]), label=r\"$\\hat{z}$\", color=cmap3[2], linestyle='--')\n",
        "    plt.axvline(x = dt*nsteps*measurement_no)\n",
        "    plt.ylabel(variable_name, fontsize=lab_size)\n",
        "    plt.xlabel('time', fontsize=lab_size)\n",
        "    plt.tick_params(axis='both', labelsize=ticksize)\n",
        "    ax.minorticks_on()\n",
        "    plt.tight_layout()\n",
        "    ax.grid(True, which='both')\n",
        "    plt.legend(fontsize=lab_size, ncol=2, framealpha=leg_alpha)\n",
        "\n",
        "    fig, ax = plt.subplots(figsize=fs)\n",
        "    plt.plot(times, state_predictions[:, 4] - state_observations[:, 4], label=r\"$\\tilde{x}$\", color=cmap3[0])\n",
        "    plt.plot(times, state_predictions[:, 5] - state_observations[:, 5], label=r\"$\\tilde{y}$\", color=cmap3[1])\n",
        "    plt.plot(times, onp.maximum(0, state_predictions[:, 6]) - state_observations[:, 6], label=r\"$\\tilde{z}$\", color=cmap3[2])\n",
        "    plt.axvline(x = dt*nsteps*measurement_no)\n",
        "    plt.ylabel(variable_name + ' error', fontsize=lab_size)\n",
        "    plt.xlabel('time', fontsize=lab_size)\n",
        "    plt.tick_params(axis='both', labelsize=ticksize)\n",
        "    ax.minorticks_on()\n",
        "    plt.tight_layout()\n",
        "    ax.grid(True, which='both')\n",
        "    plt.legend(fontsize=lab_size, framealpha=leg_alpha)\n",
        "  elif variable_name == 'linear velocity':\n",
        "    fig, ax = plt.subplots(figsize=fs)\n",
        "    plt.plot(times, state_observations[:, 7], label=r\"$v_x$\",      color=cmap3[0])\n",
        "    plt.plot(times, state_observations[:, 8], label=r\"$v_y$\",      color=cmap3[1])\n",
        "    plt.plot(times, state_observations[:, 9], label=r\"$v_z$\",      color=cmap3[2])\n",
        "    plt.plot(times, state_predictions[:, 7], label=r\"$\\hat{v}_x$\", color=cmap3[0], linestyle='--')\n",
        "    plt.plot(times, state_predictions[:, 8], label=r\"$\\hat{v}_y$\", color=cmap3[1], linestyle='--')\n",
        "    plt.plot(times, state_predictions[:, 9], label=r\"$\\hat{v}_z$\", color=cmap3[2], linestyle='--')\n",
        "    plt.axvline(x = dt*nsteps*measurement_no)\n",
        "    plt.ylabel(variable_name, fontsize=lab_size)\n",
        "    plt.xlabel('time', fontsize=lab_size)\n",
        "    plt.tick_params(axis='both', labelsize=ticksize)\n",
        "    ax.minorticks_on()\n",
        "    plt.tight_layout()\n",
        "    ax.grid(True, which='both')\n",
        "    plt.legend(fontsize=lab_size, ncol=2, framealpha=leg_alpha)\n",
        "\n",
        "    fig, ax = plt.subplots(figsize=fs)\n",
        "    plt.plot(times, state_predictions[:, 7] - state_observations[:, 7], label=r\"$\\tilde{v}_x$\", color=cmap3[0])\n",
        "    plt.plot(times, state_predictions[:, 8] - state_observations[:, 8], label=r\"$\\tilde{v}_y$\", color=cmap3[1])\n",
        "    plt.plot(times, state_predictions[:, 9] - state_observations[:, 9], label=r\"$\\tilde{v}_z$\", color=cmap3[2])\n",
        "    plt.ylabel(variable_name + ' error', fontsize=lab_size)\n",
        "    plt.axvline(x = dt*nsteps*measurement_no)\n",
        "    plt.xlabel('time', fontsize=lab_size)\n",
        "    plt.tick_params(axis='both', labelsize=ticksize)\n",
        "    ax.minorticks_on()\n",
        "    plt.tight_layout()\n",
        "    ax.grid(True, which='both')\n",
        "    plt.legend(fontsize=lab_size, framealpha=leg_alpha)\n",
        "  elif variable_name == 'angular velocity':\n",
        "    fig, ax = plt.subplots(figsize=fs)\n",
        "    plt.plot(times, state_observations[:, 10], label=r\"$w_x$\",      color=cmap3[0])\n",
        "    plt.plot(times, state_observations[:, 11], label=r\"$w_y$\",      color=cmap3[1])\n",
        "    plt.plot(times, state_observations[:, 12], label=r\"$w_z$\",      color=cmap3[2])\n",
        "    plt.plot(times, state_predictions[:, 10], label=r\"$\\hat{w}_x$\", color=cmap3[0], linestyle='--')\n",
        "    plt.plot(times, state_predictions[:, 11], label=r\"$\\hat{w}_y$\", color=cmap3[1], linestyle='--')\n",
        "    plt.plot(times, state_predictions[:, 12], label=r\"$\\hat{w}_z$\", color=cmap3[2], linestyle='--')\n",
        "    plt.axvline(x = dt*nsteps*measurement_no)\n",
        "    plt.ylabel(variable_name, fontsize=lab_size)\n",
        "    plt.xlabel('time', fontsize=lab_size)\n",
        "    plt.tick_params(axis='both', labelsize=ticksize)\n",
        "    ax.minorticks_on()\n",
        "    plt.tight_layout()\n",
        "    ax.grid(True, which='both')\n",
        "    plt.legend(fontsize=lab_size, ncol=3, framealpha=leg_alpha)\n",
        "\n",
        "    fig, ax = plt.subplots(figsize=fs)\n",
        "    plt.plot(times, state_predictions[:, 10] - state_observations[:, 10], label=r\"$\\tilde{w}_x$\", color=cmap3[0])\n",
        "    plt.plot(times, state_predictions[:, 11] - state_observations[:, 11], label=r\"$\\tilde{w}_y$\", color=cmap3[1])\n",
        "    plt.plot(times, state_predictions[:, 12] - state_observations[:, 12], label=r\"$\\tilde{w}_z$\", color=cmap3[2])\n",
        "    plt.axvline(x = dt*nsteps*measurement_no)\n",
        "    plt.ylabel(variable_name + ' error', fontsize=lab_size)\n",
        "    plt.xlabel('time', fontsize=lab_size)\n",
        "    plt.tick_params(axis='both', labelsize=ticksize)\n",
        "    ax.minorticks_on()\n",
        "    plt.tight_layout()\n",
        "    ax.grid(True, which='both')\n",
        "    plt.legend(fontsize=lab_size, ncol=3, framealpha=leg_alpha)\n",
        "\n",
        "def make_parameter_plot(nframes: int, nsteps: int, dt: float, parameters: jnp.ndarray, measurement_no: int):\n",
        "  \"\"\" Produces a plot of the parameters over time. \"\"\"\n",
        "  times = dt*nsteps*onp.arange(nframes+1)\n",
        "  fig, ax = plt.subplots(figsize=fs)\n",
        "  plt.ylabel('parameters', fontsize=title_size)\n",
        "  plt.xlabel('time', fontsize=lab_size)\n",
        "  for ii in range(parameters.shape[1]):\n",
        "    plt.plot(times[:-1], parameters[:, ii], color=cmap_ps[ii])\n",
        "  plt.tick_params(axis='both', labelsize=ticksize)\n",
        "  ax.minorticks_on()\n",
        "  ax.grid(True, which='both')\n",
        "  plt.axvline(x = dt*nsteps*measurement_no)\n",
        "  plt.tight_layout()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "height": 1000
        },
        "executionInfo": {
          "elapsed": 1958,
          "status": "ok",
          "timestamp": 1621550428641,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "tmb1sO0p0uZb",
        "outputId": "5117928c-5941-491b-ac45-389a78c9a874"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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LioPybtXx9wWE5t37826bwvuVyRUFXvn6kvFm5OKcMWK9yw8+iBeV8wfvE/P9lOgYAM+e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\nQgiR5kiBI4QQQog05/9dR1Fhp1v2+wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cFigure size 800x500 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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5GDx4MBwdHYvsc3JywpAhQzBv3rwye3TxwcvLC/369St2uU8mk6Fdu3YAwKngYlkWGzdu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\nyGQiSKUiiKUAGBYanRZqnRYanRYaVgu11vBRA40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g+cZdHDsUi52/HSzyMydMGYVWbcNw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\nCQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cFigure size 800x500 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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SExMNipuff/4Zx44da8TeERERUUOIKnCsrKywcOFCnD59GqdPn8af//xn/diwYcOQlZWF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\nSUVORK5CYII=\n",
            "text/plain": [
              "\u003cFigure size 800x500 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "### Visualize the results.\n",
        "measurement_no = 33\n",
        "make_prediction_comparison_plot(nsteps*nframes+1, dt, state_observations, predictor_states, measurement_no, 'linear velocity')\n",
        "make_parameter_plot(nframes, nsteps, dt, params_over_time, measurement_no)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oz--TV2CFZ0M"
      },
      "source": [
        "## Dynamics prediction with rotational dynamics\n",
        "\n",
        "Here we consider performing dynamics prediction for a system with nontrivial rotational dynamics. PyBullet makes it a bit difficult to do this, and also has a different integration system than our predictor. To simplify the problem, and to avoid these integration differences, we implement the rotational dynamics ourselves.\n",
        "\n",
        "We will implement the \"ground truth\" rotational dynamics in the world frame, meaning that we have to keep track of a changing moment of inertia tensor using the parallel axis theorem. We will then take observations from a rollout of this system. The predictor will implement the translational dynamics in the world frame and the rotational dynamics in the body frame."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XoohTjjrFqRx"
      },
      "outputs": [],
      "source": [
        "# moment of inertia matrix for an ellipse.\n",
        "J_def = jnp.array([[5.0, 1.0, 0], \n",
        "                   [1.0, 2, 0], \n",
        "                   [0, 0, 0.5]])\n",
        "\n",
        "# mass of the object\n",
        "m_def = 1.0\n",
        "\n",
        "# drag and magnus terms.\n",
        "Cd = 0.5\n",
        "Cl = 0.5\n",
        "\n",
        "def rotational_dynamics_body(x, u, t, J=J_def):\n",
        "  \"\"\" Implements rotational dynamics w.r.t the center of mass in the body frame.\"\"\"\n",
        "  q, p, v, w = x[:4], x[4:7], x[7:10], x[10:]\n",
        "  qdot = .5 * vector_multiply(w, q)\n",
        "  pdot = v\n",
        "  R = to_rotation_matrix(q)\n",
        "  w_world = R @ w\n",
        "  vdot = grav - Cd*jnp.linalg.norm(v)*v + Cl*jnp.cross(w_world, v)\n",
        "  wdot = -jnp.linalg.inv(J) @ jnp.cross(w, J @ w)\n",
        "  \n",
        "  return jnp.concatenate((qdot, pdot, vdot, wdot))\n",
        "  \n",
        "#disc_rot_dyn = jax.jit(rk4(rotational_dynamics, dt=dt))\n",
        "disc_rot_dyn = jax.jit(rk4(rotational_dynamics_body, dt=dt))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "executionInfo": {
          "elapsed": 19202,
          "status": "ok",
          "timestamp": 1621551017948,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "zE_gzR_ZH6E2",
        "outputId": "afd8a821-2684-48ab-b24d-40419bd72cff"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
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          ]
        }
      ],
      "source": [
        "# initialize with nontrivial rotational dynamics.\n",
        "q_init = jnp.array([0, 0, 0, 1])\n",
        "p_init = jnp.array([0, 0, 10.0])\n",
        "v_init = jnp.array([1.5, 0.0, 2.5])\n",
        "w_init = jnp.array([3.0, 2.0, 1.0])\n",
        "x_init = jnp.concatenate((q_init, p_init, v_init, w_init))\n",
        "\n",
        "# construct the adaptive predictor\n",
        "predictor = AdaptivePredictor(predictor_continuous, measurement_function, adapt_continuous, norm_state, \n",
        "                              x_init, init_params, n_features, dt, nsteps, nframes, potentials, \n",
        "                              potential_params, prediction_index=nframes)\n",
        "\n",
        "# store the state of the predictor and the parameters over the entire trajectory.\n",
        "predictor_states = []\n",
        "params_over_time = onp.zeros((nframes, nparams))\n",
        "params_over_time[0, :] = init_params\n",
        "\n",
        "# store the pybullet state over time\n",
        "state_observations = onp.zeros((1+nsteps*nframes, 13))\n",
        "state_observations[0, :] = x_init\n",
        "\n",
        "# rollout the simulation\n",
        "state_observation = x_init\n",
        "xt = x_init\n",
        "for t in range(nsteps*nframes):\n",
        "  xt = disc_rot_dyn(xt, 0, t)\n",
        "\n",
        "  # incorporate the measurement and update the parameters\n",
        "  new_measurement = (t % nsteps) == 0\n",
        "  if new_measurement:\n",
        "    ind = int(t / nsteps)\n",
        "    predictor.update_state(state_observation)\n",
        "    predictor_states.append(predictor.state_prediction.copy())\n",
        "    params_over_time[ind, :] = predictor.params\n",
        "\n",
        "  # save the state observations over time for direct comparison\n",
        "  state_observation = xt\n",
        "  state_observations[t+1, :] = xt\n",
        "\n",
        "  print(\"Finished iteration %d\" % t)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "height": 726
        },
        "executionInfo": {
          "elapsed": 1485,
          "status": "ok",
          "timestamp": 1621551019627,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "Hz2hJ8uClZMC",
        "outputId": "9a157822-1b5d-4422-a803-ae0177578f84"
      },
      "outputs": [
        {
          "data": {
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3H+XBAfcBkJaaiVarRm9/4wHQgiAIgmBNosCpBZx1etr61KOtTz1MkonzuWnEZpwnLusi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\nCxwiIiIyOSxwiIiIyOSwwCEiIiKT8//4tV3WKtmLiQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cFigure size 800x500 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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tO3yRlXsD6Ne6PsM6NsnrY2mmQi6T4eZkx/ujeiCXP1ny8J7bZ0nQpD6YdpJj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\n",
            "text/plain": [
              "\u003cFigure size 800x500 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "### Visualize the results.\n",
        "measurement_no = 34\n",
        "make_prediction_comparison_plot(nsteps*nframes+1, dt, state_observations, predictor_states, measurement_no, 'linear velocity')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kq1gGXBC2utT"
      },
      "outputs": [],
      "source": [
        "make_parameter_plot(nframes, nsteps, dt, params_over_time, measurement_no)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "last_runtime": {
        "build_target": "",
        "kind": "local"
      },
      "name": "AdaptivePrediction.ipynb",
      "provenance": [
        {
          "file_id": "1jLWfSfy177bQqxgR9ERHYz8mj7jp8Jy4",
          "timestamp": 1621549343455
        }
      ]
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
